Linear dependency between ε and the input noise in ε-support vector regression

In using the ε-support vector regression (ε-SVR) algorithm, one has to decide a suitable value for the insensitivity parameter ε. Smola et al. considered its "optimal" choice by studying the statistical efficiency in a location parameter estimation problem. While they successfully predicted a linear scaling between the optimal ε and the noise in the data, their theoretically optimal value does not have a close match with its experimentally observed counterpart in the case of Gaussian noise. In this paper, we attempt to better explain their experimental results by studying the regression problem itself. Our resultant predicted choice of ε is much closer to the experimentally observed optimal value, while again demonstrating a linear trend with the input noise.